The Trustees of the Chicago Painters and Decorators Pension, Health and Welfare and Deferred Savings Plan Trust Funds (“Trustees”) sued an employer of its union members, Royal International *785 Drywall & Decorating, Incorporated (“Royal”). The Trustees claimed that Royal violated collective bargaining agreements by failing to compensate the Funds for each hour the covered employees worked. Following a bench trial, the district court found that Royal owed contributions to the Funds and, after further proceedings, entered an award for damages. Royal appeals, contesting the admission of expert testimony at trial, the district court’s factual findings, and the amount of liquidated damages awarded. We affirm.
I.
The district court fully recounted the background of this case in its findings issued after the bench trial, so we recite the facts only as necessary.
See Trustees of the Chicago Painters v. Darwan,
No. 01-C-2458,
At trial, the Trustees claimed that Royal’s time sheets inaccurately recorded the hours worked, and were instead rigged to reflect the hours budgeted for the project. To prove the actual number of hours worked, the Trustees offered evidence of a “materials audit” that the Trustees conducted on Royal. The audit used the amount of raw materials Royal purchased for installation to calculate the amount of drywall installed. Then, the number of hours worked was calculated based on the average rate of drywall installation for a taper. The parties vigorously contested the average rate at which a taper works. Royal also contended that its time sheets were accurate and sufficient to calculate the contributions.
After hearing the evidence, the district court determined that Royal’s time sheets for its employees did “not accurately reflect hours actually worked.” Accordingly, the court had to establish an alternative means of ascertaining the hours worked in order to determine the proper amount of contributions due to the Funds. The district court, after considering testimony from experts, employees, and various published sources, followed the materials audit and settled on a rate of 2.86 boards of drywall per hour. The determination of this rate is the crux of this appeal. Based on this rate, and following further briefing from the parties, the district court awarded the Trustees $30,508.13 in unpaid contributions and $68,266.16 in liquidated damages for the period of October 1, 1999, through March 31, 2000. The district court also awarded the Trustees $17,955.82 in liquidated damages for late contributions and $712.08 in owed disbursements for the period of December 1, 1998, through March 31, 2000. Royal appeals.
II.
In an appeal from a bench trial, “[w]e review a district court’s conclusions of law de novo, and we review its findings of fact, as well as applications of law to those findings of fact, for clear error.”
Reach v. U.S. Trust Co.,
*786
On appeal, Royal first objects to the district court’s finding that the time sheets Royal maintained for its employees were inaccurate. . An employer must “maintain records with respect to each of his employees sufficient to determine the benefits due or which may become due to such employees.” 29 U.S.C. § 1059(a)(1). The collective bargaining agreement in this case required Royal to contribute benefits based on the hours worked. Therefore Royal had an obligation to maintain records of the hours worked that would be “sufficient to determine the benefits due.”
Id.
Royal did maintain time sheets; simply maintaining time sheets, however, is not enough to comply with the statute unless the time sheets are sufficient to determine the actual hours worked, and thus the benefits due. Previous cases in this circuit have characterized sufficient records as “reliable, contemporaneous records,”
Chicago Dist. Council of Carpenters Pension Fund v. Reinke Insulation Co.,
Royal claims that it properly main-' tained reliable, contémporaneous time sheets reflecting the hours worked. The district court, however, made extensive findings about the insufficient quality of Royal’s time sheets and records. Specifically, the district court noted that “only five of the 263- time sheets for the period [at issue] record daily hours worked; the remainder list only weekly totals.” While weekly, instead of daily, totals of hours are not necessarily insufficient under the agreement, other evidence raised suspicion that the weekly totals were inaccurate. For example, the district court noted that the hours budgeted and the hours worked on the time sheets matched on a substantial majority of the time sheets. The district court also remarked on various notations made on the time sheets, such as “a hand written calculation dividing the number of hours budgeted (156.25) by the number of crew members' (4); the sheet assigns 39.25 hours to [the crew chief], while each remaining crew member is reported to have worked only 39 hours.” Furthermore, employees testified that they regularly worked more hours than were reflected on the time sheets, and the district court found their testimony credible. Although Royal presents alternative explanations for the quality of the time sheets, the district court’s conclusion reflects a reasonable examination of the evidence and testimony. We are not “left with the definite and firm conviction that a mistake has been committed.”
Gaffney v. Riverboat Servs. of Indiana,
Because Royal’s records were insufficient, the district court proceeded to
*787
seek another method for determining the number of hours the employees worked in order to calculate the proper benefits. It did so by finding an hourly rate at which drywall tapers installed drywall boards, a rate that the parties vigorously contested before the district court. On appeal, Royal objects to the district court’s admission of the testimony of two experts,
2
John Hull and Ian Parr, who offered their opinions on the rate of drywall taping. We review de novo the district court’s application of the principles articulated in
Daubert v. Merrell Dow Pharmaceuticals, Inc.,
Following this standard, we first examine whether the district court applied the proper framework. This step “evaluates the reliability of the testimony” and should “reject any subjective belief or speculation.”
Ammons,
Next we examine whether the experts’ testimony would assist the trier of fact. The district court referred to
Daubert
in admitting the experts and noted that, in the context of a bench trial, the judge would be able to consider any shortcomings of their expertise drawn out through cross-examination.
See In re Salem,
Since the district court applied the proper framework, we next consider whether the district court abused its discretion in admitting the testimony of the experts. The district court aptly observed in overruling Royal’s objection to Hull’s testimony as an expert that he
worked for many years in the industry, directly, himself, taping drywall, and now training for more than 10 years, all the apprentices in the area, including those employed by the defendant himself. If this gentleman is not an expert on the issue of how much can be reasonably expected [of] a drywall taper to do in a day, I don’t know [if] there is such a person.
Regarding Parr, the district court observed that “[t]his is a gentleman who does cost estimating on a regular basis, he uses a source that’s widely recognized and agreed to in the construction industry .... [and] has done [cost estimating] for 30 years.” The district court exercised discretion in admitting the experts, and we find no abuse in admitting the testimony of these two individuals as experts at trial. Royal’s objections are therefore without merit.
Royal next contends that the district court clearly erred in determining the productivity rate to be 2.86 boards per hour. Royal pointed out a number of inconsistencies and inadequacies in the Trustees’ witnesses’ testimony and in the documentary evidence. Contrary to Royal’s assertion, the determination of the productivity rate is a factual question separate from a legal interpretation of a collective bargaining agreement, and is therefore reviewed for clear error.
Reach,
Finally, in a cursory, two-paragraph argument in its opening brief, without citations to the record or authority, Royal asserts that the district court’s award of liquidated damages for late payments in the amount of $17,955.82 was without support in the record. We could consider such “unsupported and undeveloped arguments” to be waived.
United States v. Turcotte,
We review the district court’s award of damages for clear error.
Wheel Masters, Inc. v. Jiffy Metal Prods. Co.,
Royal similarly objects to the Trustees’ reliance on the final audit report, arguing that the Trustees were required to show each tardy payment, not just the total amounts. As discussed above, however, the Trustees did produce evidence of the total amount of liquidated damages through the final audit and the requested supplemental briefing, and further elicited from Royal’s owner that he had no basis to dispute the totals. While Royal remained free to produce evidence to contradict the Trustees’ evidence, sufficient evidence was present in the record at trial and in the supplemental briefing for the district court to discern an amount of liquidated damages without committing clear error. Royal’s argument is therefore without merit.
Royal also asserts that it cannot be held liable for liquidated damages because the Trustees’ complaint did not properly plead a claim for such damages. This is a distinct argument against the award of liquidated damages and Royal did not present this argument in its opening brief. This argument is therefore forfeited.
NLRB v. IBEW, Local Union 16,
III.
The district court did not commit clear error in finding that Royal’s time sheets were insufficient or in determining the productivity rate from which the contributions to the Funds could be calculated. Additionally, the district court did not abuse its discretion in admitting expert testimony to assist the trier of fact in determining the rate of drywall installation to be used. Furthermore, the district court did not clearly err in awarding the Trustees liquidated damages. Accordingly, we AffiRM the judgment of the district court.
Notes
. Royal argues that the district court’s determination that the time sheets were sufficient should be reviewed de novo. The sufficiency of time sheets, however, is a factual question requiring the district court to determine whether the time sheets are, in fact, accurate. Further determining whether those time sheets are sufficient to ascertain benefits requires an application of the law to the facts. Both findings are reviewed for clear error.
Reach,
. Royal also argues that a third individual, Steven Klomfar, should not have been admitted as an expert. Klomfar, however, was not offered as an expert and testified as a factual witness based on his personal knowledge. Royal also mentions a fourth individual in this section of its brief, Howard Levinson, an accountant who conducted the materials audit. Levinson similarly was not offered as an expert at trial, and he did not propose a productivity rate of his own. Instead, Levin-son used a rate provided by others and testified as to his own knowledge of the audit process. We therefore need not conduct a Daubert analysis of the testimony of Klomfar or Levinson.
. Royal complains that the district court's liquidated damages award was based on a document and affidavit tendered to the court in response to the district court’s request for additional briefing on damages, but which was not admitted at trial. Royal contends that only documents admitted at trial could be considered in the supplemental briefing. Regardless, the critical document listing the amount of liquidated damages was admitted at trial as Plaintiff's Exhibit 15. Supplementation of the trial record before the district court, which Royal argues the Trustees should have done, was arguably unnecessary. Furthermore, if the district court desired to consider such additional evidence (as it apparently did by citing to it in its decision), such "decisions regarding the admission and exclusion of evidence are peculiarly within the competence of the district court.”
Adams v. City of Chicago,
